Open AccessOn Boundary Value Problems for a Mixed Type Fractional Differential Equation with Caputo Operator
Author(s) -
T. K. Yuldashev,
Б.И. Исломов,
U.Sh. Ubaydullaev
Publication year - 2021
Publication title -
ķaraġandy universitetìnìn̦ habaršysy. matematika seriâsy
Language(s) - English
Resource type - Journals
eISSN - 2663-5011
pISSN - 2518-7929
DOI - 10.31489/2021m1/127-137
Subject(s) - mathematics , boundary value problem , mathematical analysis , eigenfunction , mixed boundary condition , operator (biology) , fourier series , partial differential equation , domain (mathematical analysis) , free boundary problem , variable (mathematics) , eigenvalues and eigenvectors , physics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene
This article is devoted to study the boundary value problems of the first and second kind with respect to the spatial variable for a mixed inhomogeneous differential equation of parabolic-hyperbolic type with a fractional Caputo operator in a rectangular domain. In the study of such boundary value problems, we abandoned the boundary value condition with respect to the first argument and instead it is used additional gluing condition. In this case, in the justification of the unique solvability of the problems, the conditions on the boundary domain are removed. This allowed us to weaken the criterion for the unique solvability of boundary value problems under consideration. The solution is constructed in the form of Fourier series with eigenfunctions corresponding to homogeneous spectral problems. Estimates for the convergence of Fourier series are obtained as a regular solution of this mixed equation.